My only real suggestion is to arrange your hexes to reduce the total number of cuts, rather than in a standard hex pattern. You waste a bit of chipboard, but man does it make it easier.

In this example, you make the big red cuts first, each of which affects 3 or 4 hexes. Then you make the blue cuts on the ensuing strips, each of which cuts 2 hexes. Then you make the green cuts, each of which affects 1 hex.

In this example, instead of the 60 cuts you'd have to make if they were in a standard hex pattern (or some other pattern), you'd only make 36 cuts. Still a lot of cuts, but a 40% savings in individual cuts is nothing to sneer at.

I use a box-cutter-like knife and steel ruler for such cutting. An X-acto knife is better for more intricate cuts, but for simple straight ones, you can't go wrong, especially if you use the break-off-blade type, where you can get a "new" blade every few cuts (for really heavy chipboard, every dozen or so cuts for lighter chipboard). I buy them at the 99-cent store, and they come with 3 extra blades, each of which breaks into about 10 blades. Sweet!

Back in architecture school, we figured out that using scalpel blades were much sharper, cheaper (or at least the same price), and lasted longer than exacto blades. So I'll just toss that advice out there. Also they are much thinner so you may need to take a few practice cuts to get used to it. But once you are used to a scalpel to cut, you'll see how much nicer they are than an exacto blade (INHO)...but be very careful..they are really sharp! Oh yeah, to use the scalpel blades you need to by the scalpel, but they are about the same price as an exacto, so no big diff.

In addition, for safety, it is good to to use a metal ruler that provides some finger protection. Also I'll second (or third): cut in long strokes with little pressure. LET THE BLADE DO THE WORK!